Sir David Garrard, who has donated £1.5 million to Labour since 2003, told the paper: “I have watched with dismay and foreboding the manner in which the leadership has, in my view, over the last two years, conducted itself.”

No let-up for Labour

Jonathan Blake, BBC political correspondent

With negative stories on the front pages of at least four newspapers, this is not a happy Easter Sunday for Labour.

The online abuse highlighted by the Sunday Times investigation shows a problem the party has with a relatively small number of people willing to use racism, misogyny and threats of violence in support of Jeremy Corbyn.

Labour has denounced the behaviour and distanced itself from the groups.

Mr Corbyn has condemned, criticised and apologised time and time again.

But after a bad week for the party, things have not improved.

The leader has admitted that Labour must “do better” in tackling anti-Semitism, but with no apparent quick fix at hand and no let-up in accusations, he has some way to go to convince everyone in his party that he has a grip on the problem.

The Sunday Times says the Facebook groups covered in its report have a membership of around 400,000 people including 12 senior staff working for Mr Corbyn and shadow chancellor John McDonnell.

Comments in the groups show members advocating violence, reports the paper.

It also said it found messages comparing the Conservatives to Nazis and suggesting a journalist should be killed.

Writing in the newspaper, Jewish Labour MP Luciana Berger said she had received an email from someone who claimed to be a party member telling her she should kill herself.

She had also been called “Judas”, “a venal piece of detritus”, a “Zionazi” and an “absolute parasite.”

A spokesman for the Labour Party said: “These groups are not run by the Labour Party or officially connected to the party in any way.”

Labour also told the Sunday Times that no-one in Mr Corbyn or Mr McDonnell’s offices has seen, posted or endorsed anti-Semitic or abusive messages.

The latest allegations mark a deepening in the row over anti-Semitism in the Labour Party which has dogged Mr Corbyn for the past week.